What is the effect of mislabeled training data?
I think the crucial point here is what you precisely mean by mislabelled. Google's image classifier will likely do a 'pretty good' job of retrieving images with the given subject included, but how strict or lenient your class requisites are is quite important. For example, if one of your classes is 'dog' there may be hundreds of images procured from scraping that could display (examples off the top of my head, but you can get even more creative): 


Ancient canine fossils
Wolves
Stuffed animal dogs
Hard mode dogs (i.e. partially occluded, variable lighting schemas, background color variation, intraclass/species variation)


Additionally, your computational tool will impact this. If you're using a neural network, the above issues can to some extent be accounted for, but a linear classifier would likely have difficulty adopting a broader/flexible view of your class.